Though the Covenant is driven by religious zeal, not all have ascribed to it. Insurrections and rebellions have happened often throughout the Covenant's long history: the Hunter problem and the Grunt Rebellion are just a couple that we know of.
The most recent organization against the powers that be saw Elites and Grunts rallying behind another Elite known only as the Heretic Leader. Further encouraged by information volunteered by the rescued 343 Guilty Spark, the Heretics set up their base on a Forerunner station and lab orbiting in the atmosphere of Threshold (that predates Halo 04 by several hundred years). Though it is uncertain how long his movement had been going on, it is from this station that he intended to spread his message. Whether the release of the Flood on the orbital platform was accidental or merely part of his plan to "make [the Elites] see" is unknown. His death seems unnecessary now, and we can only hope that his onetime followers will hold no grudge against the Arbiter, and rally behind the Elites left over from the now fractured Covenant.
Are you a good samaritan? Do Engineers run from you, or can you creep a little closer? A little discussion on the forum shows that even the most bloodthirsty ODST can turn Attenborough . . .